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krek1111 [17]
3 years ago
15

Find the solution to the system of equations y=x-4 and y=4x+2

Mathematics
2 answers:
dmitriy555 [2]3 years ago
7 0

The answer is y=x-4=4x+2

gogolik [260]3 years ago
4 0

The answer will be

I solve by substitution

(-2, -6)

X=-2, y=-6

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dsp73

To solve this question, you would need to find the common denominator among the 2 fractions. In this case it would be

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5 0
3 years ago
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What is the quadratic regression equation for the data set? ​ ​ ​ <br><br> PLEASEE HELP ME
Soloha48 [4]
You're trying to find constants a_0,a_1,a_2 such that \hat y=a_0+a_1\hat x+a_2{\hat x}^2. Equivalently, you're looking for the least-square solution to the following matrix equation.


\underbrace{\begin{bmatrix}1&6&6^2\\1&3&3^2\\\vdots&\vdots&\vdots\\1&9&9^2\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}100\\110\\\vdots\\70\end{bmatrix}}_{\mathbf b}

To solve \mathbf{Ax}=\mathbf b, multiply both sides by the transpose of \mathbf A, which introduces an invertible square matrix on the LHS.

\mathbf{Ax}=\mathbf b\implies\mathbf A^\top\mathbf{Ax}=\mathbf A^\top\mathbf b\implies\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b

Computing this, you'd find that

\mathbf x=\begin{bmatrix}a_0\\a_1\\a_2\end{bmatrix}\approx\begin{bmatrix}121.119\\-3.786\\-0.175\end{bmatrix}

which means the first choice is correct.
8 0
4 years ago
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